Eric Riemer Hare
Eric Hare
Iowa State University
April 5th, 2017
Statistical Methods for Bullet Matching
Papers:
Eric Hare, Heike Hofmann, Alicia Carriquiry
Center for Statistics and Applications in Forensic Evidence (CSAFE)
The problems culminated in a 2009 NAS report which found “much forensic evidence – including, for example, bite marks and firearm and toolmark identification is introduced in criminal trials without any meaningful scientific validation, determination of error rates, or reliability testing.” (National Research Council 2009)
From a September 2016 report by the President’s Council of Advisors on Science and Technology (PCAST) titled Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-Comparison Methods (Advisors on Science and Technology 2016):
A second—and more important—direction is (as with latent print analysis)
to convert firearms analysis from a subjective method to an objective
method. This would involve developing and testing image-analysis
algorithms for comparing the similarity of tool marks on bullets. [...]
In a recent study, researchers used images from an earlier study to
develop a computer-assisted approach to match bullets that minimizes
human input [338].
338: Hare, E., Hofmann, H., and A. Carriquiry. “Automatic matching of bullet lands.” Unpublished paper, available at: arxiv.org/pdf/1601.05788v2.pdf.
The key to this approach is the reference database…
plot3D.x3p.file(read_x3p("../images/Hamby (2009) Barrel/bullets/Br1 Bullet 1-5.x3p"),
plot.type = "surface")We need to choose a location (height) of the bullet at which to extract a profile. To do so, we optimize the CCF (T. Vorburger et al. 2011):
Parameters: d = 25μm, d0 = 25μm, c = 0.9
br111 <- get_crosscut("images/Br1 Bullet 1-5.x3p", x = 243.75)
qplot(y, value, data = br111) + theme_bw()The striations that identify a bullet to a gun barrel are located in the land impression areas (Xie et al. 2009).
Parameters: s = 35μm
br111.groove <- get_grooves(br111)
br111.groove$plotresult2 <- get_grooves(get_crosscut("../images/Hamby (2009) Barrel/bullets/Br1 Bullet 1-6.x3p"))
result2$plotLocal weighted scatterplot smoothing (Cleveland 1979) - Fits a low-degree polynomial to a small subset of the data, weighting values near the point to be estimated more strongly.
br111.loess <- fit_loess(br111, br111.groove)
br111.loess$fittedDeviations from the loess fit should represent the imperfections (striations) on the bullet. Hence, we extract the residuals from the model.
br111.loess$residAs with detecting the shoulders, we can smooth the deviations and compute derivatives to identify peaks and valleys in the signature.
br111.peaks <- get_peaks(br111.loess$data)
br111.peaks$plotThe previous five steps are performed for each bullet land. But now we wish to extract features for cross comparisons of bullet lands.
Features are extracted from each land-to-land comparison:
Verbatim from September:
We have steps to address each of these concerns…
NIST has provided some more data:
To begin to tackle the degraded bullet problem, we need to standardize features by the length of the recovered land.
Matches = 27, Matches per mm = 14.72
By standardizing the features, we don’t penalize the degraded case as in the first revision of our algorithm:
Matches = 8, Matches per mm = 11.42
Simulation Study:
https://isu-csafe.stat.iastate.edu/shiny/bulletr/
https://isu-csafe.stat.iastate.edu/shiny/bullets/
Special thanks to Alan Zheng at the National Institute of Standards and Technology for maintaining the NIST Ballistics Toolmark Research Database and providing many useful suggestions for our algorithm.
Any Questions?
Advisors on Science, President’s Council of, and Technology. 2016. “Report on Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-Comparison Methods.” https://www.whitehouse.gov/sites/default/files/microsites/ostp/PCAST/pcast_forensic_science_report_final.pdf.
Biasotti, Alfred A. 1959. “A Statistical Study of the Individual Characteristics of Fired Bullets.” Journal of Forensic Sciences 4 (1): 34–50.
Chu, Wei, Robert M Thompson, John Song, and Theodore V Vorburger. 2013. “Automatic identification of bullet signatures based on consecutive matching striae (CMS) criteria.” Forensic Science International 231 (1–3): 137–41.
Clarkson, James A, and C Raymond Adams. 1933. “On Definitions of Bounded Variation for Functions of Two Variables.” Transactions of the American Mathematical Society 35 (4). JSTOR: 824–54.
Cleveland, William S. 1979. “Robust Locally Weighted Regression and Smoothing Scatterplots.” Journal of the American Statistical Association 74 (368). Taylor & Francis, Ltd.: 829–36. http://www.jstor.org/stable/2286407.
Giannelli, Paul C. 2011. “Ballistics Evidence Under Fire.” Criminal Justice 25 (4): 50–51.
Hamby, James E., David J. Brundage, and James W. Thorpe. 2009. “The Identification of Bullets Fired from 10 Consecutively Rifled 9mm Ruger Pistol Barrels: A Research Project Involving 507 Participants from 20 Countries.” AFTE Journal 41 (2): 99–110.
Hofmann, Heike, and Eric Hare. 2016. Bulletr: Algorithms for Matching Bullet Lands.
National Research Council. 2009. Strengthening Forensic Science in the United States: A Path Forward. Washington, DC: The National Academies Press. doi:10.17226/12589.
Nichols, Ronald G. 2003. “Consecutive Matching Striations (CMS): Its Definition, Study and Application in the Discipline of Firearms and Tool Mark Identification.” AFTE Journal 35 (3): 298–306.
OpenFMC. 2014. X3pr: Read/Write Functionality for X3p Surface Metrology Format.
Vorburger, T.V., J.-F. Song, W. Chu, L. Ma, S.H. Bui, A. Zheng, and T.B. Renegar. 2011. “Applications of Cross-Correlation Functions.” Wear 271 (3–4): 529–33. doi:http://dx.doi.org/10.1016/j.wear.2010.03.030.
Xie, F., S. Xiao, L. Blunt, W. Zeng, and X. Jiang. 2009. “Automated Bullet-Identification System Based on Surface Topography Techniques.” Wear 266 (5–6): 518–22. doi:http://dx.doi.org/10.1016/j.wear.2008.04.081.